Introduction to Heavy Meson Decays and CP Asymmetriesligeti/talks/ssi.pdf · Central questions...
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Introduction to Heavy Meson Decays and CP Asymmetries Zoltan Ligeti Lawrence Berkeley Laboratory Thanks to: Adam Falk, Sandrine Laplace, Mike Luke, Yossi Nir
Transcript of Introduction to Heavy Meson Decays and CP Asymmetriesligeti/talks/ssi.pdf · Central questions...
Introduction to Heavy Meson Decaysand CP Asymmetries
Zoltan LigetiLawrence Berkeley Laboratory
Thanks to: Adam Falk, Sandrine Laplace, Mike Luke, Yossi Nir
References
An incomplete list:
• Y. Nir, hep-ph/0109090
• A. Falk, hep-ph/0007339
• The Babar Physics Book, SLAC-R-0504
• B Physics at the Tevatron: Run II and Beyond, hep-ph/0201071
• Manohar and Wise, Heavy Quark Physics, Cambridge Monogr. Part. Phys.Nucl. Phys. Cosmol. 10 (2000)
• Bigi and Sanda, CP Violation, Cambridge University Press, New York, 2000
• Branco, Lavoura and Silva, CP Violation, Clarendon Press, Oxford, 1999
Z L — SSI p.1/i
Disclaimers
In these lectures:
... I will not talk about the strong CP problem see: H. Quinn, hep-ph/0110050M. Dine, hep-ph/0011376
L =θQCD16π2
FµνFµν
... I will not talk about lattice QCD see: lectures of P. Lepage
... I will not talk about beyond SM physics see: lectures of A. Kagan
Z L — SSI p.1/ii
Dictionary
• SM = standard model
• NP = new physics
• CPV = CP violation/violating
• CPC = CP conserving
• UT = unitarity triangle
Z L — SSI p.1/iii
Central questions about SM
1. Origin of electroweak symmetry breaking:
SU(2)L × U(1)Y → U(1)EM
spontaneous breaking of a gauge symmetry by v ∼ 250 GeV VEV
WLWL →WLWL breaks unitarity ∼ 1 TeV ... determines scale of Higgs / NP
2. Origin of flavor symmetry breaking:
U(3)Q × U(3)u × U(3)d → U(1)Baryon (for leptons don’t even know yet!)
global symmetries (e.g, dR, sR, bR identical if massless) broken by dimension-less Yukawa couplings ... we do not know what scale to look
It would be nice if flavor and electroweak symmetry breaking were connected
Flavor physics depends on both — Yukawa couplings determine quark masses,mixing, and CP violation
Z L — SSI p.1/iv
Central questions of flavor physics
1. Does the SM (i.e., only virtual quarks, W , and Z interacting through CKMmatrix in tree and loop diagrams) explain all flavor changing interactions?
2. If it does not, then at what level and where can we see deviations?
To answer these questions, we need: Experimental precisionTo answer these questions, we need: Theoretical precision — cleanliness
corollary:
The point is not simply to measure CKM elements, but to overconstrain the SMdescription of flavor by many “redundant” measurements
The key processes are those which can teach us about high energy phsyicswithout hadronic uncertainties
Z L — SSI p.1/v
Interplay between weak and strong interactions
• Can we learn about high energy physics from low energy hadronic processes?
QCD coupling is scale dependent:
αs(µ) =αs(M)
1 +αs2π
β0 lnµ
M
High energy (short distance): perturbation theory is useful
Low energy (long distance): QCD becomes nonperturbative ⇒ It is usually veryhard, if not impossible, to make precise calculations
• Solutions: – Use symmetries of QCD (exact or approximate)
Solutions: – Certain processes are determined by short-distance physics
Sometimes it is possible to use data and symmetries together to eliminate uncal-culable hadronic mess
Z L — SSI p.1/vi
(1) Want to learn about CP violation
• sin(2β) from B → ψKS :
c
ψ
KS
B
c
s
d
b
energy release:mB −mψ −mK ' 1.7 GeV
Contributions of diagrams with manysoft gluons are not suppressed
Theoretically clean measurement of sin(2β) possible (at < 1% level), becauseamplitudes with one weak phase dominate
• Solution: CP symmetry of strong interactions (exact symmetry)
Solution: The magnitude of the amplitude does not matter, only need the relation:
Solution: 〈ψKS|H|B0〉 = −〈ψKS|H|B0〉 × [1 +O(αsλ2)]
Z L — SSI p.1/vii
(2) Want to learn about CKM elements
• |Vcb| from B → D(∗)`ν :
ν
�����
Contributions of diagrams with manysoft gluons are not suppressed
Theoretically clean measurement of |Vcb| possible (at 5% level), because hadronicmatrix element is known in the mc,b →∞ limit at “zero recoil” v · v′ = 1
• Solution: Heavy quark symmetry in heavy mesons (approximate symmetry)
Solution: determines rate at zero recoil: 〈D∗(v)|J |B(v)〉 = 1 +O( Λ2
QCD
(2mc)2
)
Z L — SSI p.1/viii
(3) Want to learn about physics beyond the SM
• E.g.: B → Xsγ:γ
Xs
B
pXs
q
t
Inclusive decay:Xs = K∗, K(∗)π, K(∗)ππ, etc.
Diagrams with many gluons are cru-cial, resumming certain subset ofthem affects rate at factor-of-two level
Rate calculable at 10% level, using several effective theories, renormalizationgroup, operator product expansion... one of the most involved SM analyses
• Solution: Short distance dominated; unknown corrections suppressed by
Solution: Γ(B → Xsγ) = [known]×{
1 +O(α3s ln
mW
mb,Λ2
QCD
m2b,c
,αs∆mc
mb
)}
Z L — SSI p.1/ix
Outline (1)
1. Introduction to flavor physics and CPV
... Brief SM review
... How CKM matrix arises from Yukawa couplings
... Present status
Mixing and CPV in neutral meson systems (K,D,B,Bs)
... Ways to obtain clean information about short distance physics
... Mixing: ∆mBd and ∆mBs
... CPV: B → ψKs, B → φKs
Z L — SSI p.1/1
Outline (2–3)
2. The heavy quark limit
... Heavy quark symmetry: spectroscopy, strong decays
... Exclusive B → D(∗)`ν decays and |Vcb| (HQET)
... Inclusive semileptonic decays, |Vcb| (OPE)
... Inclusive |Vub| measurements and rare decays
3. Some clean CP measurements
... Bs → DsK, B → ππ isospin analysis, B → DK
Nonleptonic decays, factorization
... Factorization in B → D(∗)X decays; tests of factorization
... Factorization in charmless decays
... Tests / applications in decays to pseudoscalars (α, γ)
Final thoughts
Z L — SSI p.1/2
Introduction
The Standard Model (SM)
Gauge symmetry: SU(3)c × SU(2)L × U(1)Y parameters
Gauge symmetry: 8 gluons W±, Z0, γ 3
Particle content: 3 generations of quarks and leptons
Particle content: QL(3, 2)1/6, uR(3, 1)2/3, dR(3, 1)−1/3 10
Particle content: LL(1, 2)−1/2, `R(1, 1)−1 3(+9)
Particle content: quarks:(u c t
d s b
)leptons:
(νe νµ ντ
e µ τ
)Symmetry breaking: SU(2)L × U(1)Y → U(1)EM
symmetry breaking: φ(1, 2)1/2 Higgs scalar, 〈φ〉 =(
0v/√
2
)2
• The SM agrees (too well...) with all observed particle physics phenomena
Z L — SSI p.1/3
Why is CPV interesting?
“CPV is a mystery”... the SM with 3-generations “predicts” it
“CPV is one of the least understood parts of the SM”... sin 2β, εK, ε′ are all in the right ballpark
BUT:
– Almost all extensions of the SM contain new sources of CP and flavor violation
– Major constraint for model building, may distinguish between NP models
– The observed baryon asymmetry of the Universe requires CPV beyond the SM(not necessarily in flavor changing processes)
If ΛCPV � ΛEW: no observable effects inB decays⇒ precise SM measurements
If ΛCPV ∼ ΛEW: sizable effects possible⇒ could get detailed information on NP
Z L — SSI p.1/4
The track record
Bits of history: KK mixing ⇒ GIM & charmBits of history: CP violation ⇒ three generations, CKMBits of history: BB mixing ⇒ heavy top
Best sensitivity to some particles predicted in the MSSM comes from (crudely...)
experiment energy scale best sensitivity to
Tevatron ∼ 2 TeV squarks, gluinosLEP ∼ 200 GeV sleptons, charginos
B → Xsγ ∼ 5 GeV charged Higgs
Z L — SSI p.1/5
SM: where can CP violation occur?
• Kinetic terms: Lkin = −14
∑groups
(F aµν)2 +
∑rep′s
ψ iD/ ψ
always CPC (ignoring FF )
• Higgs terms: LHiggs = |Dµφ|2 + µ2φ†φ− λ(φ†φ)2 (v2 = µ2/λ)CPC if ∃ only one Higgs doublet; CPV possible with extended Higgs sector
• Yukawa couplings in interaction basis:
LY = −Y dijQILi φdIRj − Y uij QILi φ uIRj − Y `ij LILi φ `IRj + h.c.
cannot write mass term for ν’s!i, j ∼ generations
↘=
(0 1
−1 0
)φ∗
CPV is related to unremovable phases of Yukawa couplings:
Yij ψLi φψRj + Y ∗ij ψRj φ†ψLi
⇓ CP exchanges fermion bilinearsYij ψRj φ
†ψLi + Y ∗ij ψLi φψRj
Z L — SSI p.1/6
Quark mixing
• Replacing φ with its VEV in Yukawa couplings:
Lmass = −(Md)ij dILi dIRj − (Mu)ij uILi u
IRj − (M`)ij `ILi `
IRj + h.c.
Mf =v√2Y f — want to diagonalize these (f = u, d, `)
Mdiagf ≡ VfLMf V
†fR — VL,R unitary matrices
Define mass eigenstates:fLi ≡ (VfL)ij f ILjfRi ≡ (VfR)ij f IRj
• The quark mass matrices are diagonalized by different transformations for uLiand dLi, which are part of the same SU(2)L doublet QL(
uILidILi
)= (V †uL)ij
(uLj
(VuLV†dL)jk dLk
), VCKM ≡ VuLV †dL
Which terms in the Lagrangian get modified by this transformation?
Z L — SSI p.1/7
SM: where can flavor violation occur?
• In mass basis, charged current (W±) weak interactions become complicated:
−g2QILi γ
µW aµ τ
aQILi + h.c. ⇒ − g√2
(uL, cL, tL
)γµW+
µ (VuLV†dL)
dL
sL
bL
+ h.c.
⇑Cabibbo-Kobayashi-Maskawa matrix: VCKM
Only source of CPV in flavor changing processes in the SM
• The neutral current (Z0) interactions remain flavor conserving in the mass basis(True in all models with only left handed doublet and right handed singlet quarks)
⇒ In the SM, only charged current interactions change flavor
Z L — SSI p.1/8
How do we know that CP is violated?
• Prior to 1964, the explanation of the large lifetime ratio of the two neutral kaonswas CP symmetry (before 1956, it was C alone...)
|K0〉 = s d , |K0〉 = d s , CP |K0〉 = +|K0〉 (convention dependent)
states of definite CP : |K1,2〉 = 1√2
(|K0〉 ± |K0〉)
states of definite CP : CP |K1〉 = |K1〉 , CP |K2〉 = −|K2〉
If CP were an exact symmetry:only K1 → ππ
both K1,2 → πππ
}⇒ τ(K1)� τ(K2)
• But KL → ππ decay was also observed (1964) at the 10−3 level!
η00 = 〈π0π0|H|KL〉〈π0π0|H|KS〉
η+− = 〈π+π−|H|KL〉〈π+π−|H|KS〉
εK ≡ 13 (η00 + 2η+−) ε′K ≡ 1
3 (η+−− η00)
Was <1 yr to propose superweak, but 9 till KM (before 2nd generation complete!)
Z L — SSI p.1/9
Baryogenesis
# baryons# photons
∼ 10−9 now ⇐⇒ nq − nqnq + nq
∼ 10−9 at t < 10−6 sec (T > 1 GeV)
• To produce such an asymmetry from symmetric initial conditions, need
1. baryon number violating interactions
2. C and CP violation
3. deviation from thermal equilibrium
• SM contains 1–3, but
A. CP violation is too small
B. deviation from thermal equilibrium too small with just one Higgs doublet
NP models can solve A–B near the weak scale, and may have observable effects(possibly only in flavor diagonal processes, such as electric dipole moments)
Z L — SSI p.1/10
Why B physics?
• Observed CPV in K system is at the right level (εK can be described with O(1)CKM phase), but hadronic uncertainties preclude precision tests (ε′K is notori-ously hard to calculate)
Plan to measure K → πνν — theoretically clean, but B ∼ 10−10(K±), 10−11(KL)
A ∝
(λ5m2
t ) + i(λ5m2t ) t : CKM suppressed
(λm2c) + i(λ5m2
c) c : GIM suppressed(λΛ2
QCD) u : GIM suppressed
� �� �
��������� �� ���
� �
� � � �� �
(hep-ph/0110255)
• In D decays the SM predicts small CPV, interesting for NP (few words later)
• In the B meson system, large variety of interesting processes:
– top quark loops neither GIM nor CKM suppressed (large mixing, rare decays)
– large CP violating effects possible, some of which have clean interpretation
– some of the hadronic physics understood model independently (mb � ΛQCD)
Z L — SSI p.1/11
CKM matrix and the unitarity triangle
• CKM matrix is hierarchical
(u, c, t)
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
d
s
b
∼ 1
∼ λ∼ λ2
∼ λ3
λ ∼ 0.22
Elements depend on 4 real parameters (3 angles + 1 CPV phase)VCKM is the only source of CPV in the SM
• The unitarity triangle provides a simple way to visualize the SM constraints
Vcd Vcb*
VudVub* Vtb
*Vtd
βγ
α
CPV in SM ∝ Area
Vud V∗ub+Vcd V
∗cb+Vtd V
∗tb = 0
The angles and sides aredirectly measurable — wantto overconstrain this picture
Z L — SSI p.1/12
Wolfenstein parameterization
• It is convenient to exhibit the hierarchical structure by expanding in λ = sin θC
V =
1− 12λ
2 λ Aλ3(ρ− iη)−λ 1− 1
2λ2 Aλ2
Aλ3(1− ρ− iη) −Aλ2 1
+O(λ4)
Present uncertainties: λ ∼ 1%, A ∼ 5%, η/ρ ∼ 7%,√ρ2 + η2 ∼ 20%,
• Constraints on CKM usually plotted on the (ρ, η) plane, ρ+ iη ≡ −VudV∗ub
VcdV∗cb
VudVub*
Vcb*Vcd Vcd
Vtd
Vcb*
Vtb*
βγ
α
(0,0)
(ρ,η)
(1,0)
β ≡ arg(−VcdV
∗cb
VtdV∗tb
)βs ≡ arg
(−VtsV
∗tb
VcsV ∗cb
)α ≡ arg
(− VtdV
∗tb
VudV∗ub
)γ ≡ arg
(−VudV
∗ub
VcdV∗cb
)
Z L — SSI p.1/13
Experimental program
• Goal: precision tests of the flavor sector via redundant measurements, which inthe SM determine CKM elements, but sensitive to different short distance physics
New physics could easily modify:
– SM loop processes: mixing
– SM loop processes: rare decays
– CP violation
So we want to measure:
– mixing & rare decays
– CPV asymmetries
– compare tree and loop processes
• In the presence of NP, many independent and large CPV phases are possible;Then “α, β, γ” is only a language and two “would-be” γ measurements can besensitive to different NP contributions (similarly for |Vtd|, |Vts|)
Do all possible measurements which have clean interpretation; correlations maybe crucial to narrow down type of NP
⇒ Very broad program — independent measurements are searching for NP!
Z L — SSI p.1/14
Present knowledge of (ρ, η)
Tree level + CP conserving only
-1
0
1
-1 0 1 2
∆md
∆ms & ∆md
|Vub/Vcb|
ρ
η
CK Mf i t t e r
p a c k a g e
Z L — SSI p.1/15
Present knowledge of (ρ, η)
Tree level + CP conserving
-1
0
1
-1 0 1 2
∆md
∆ms & ∆md
|Vub/Vcb|
ρ
η
CK Mf i t t e r
p a c k a g e
Tree level + CP violating
-1
0
1
-1 0 1 2
sin 2βWA
εK
εK
|Vub/Vcb|
ρ
η
CK Mf i t t e r
p a c k a g e
Z L — SSI p.1/15
Present knowledge of (ρ, η)
Tree level + CP conserving + εK
-1
0
1
-1 0 1 2
∆md
∆ms & ∆md
εK
εK
|Vub/Vcb|
ρ
η
CK Mf i t t e r
p a c k a g e
Tree level + CP violating
-1
0
1
-1 0 1 2
sin 2βWA
εK
εK
|Vub/Vcb|
ρ
η
CK Mf i t t e r
p a c k a g e
Z L — SSI p.1/15
Present knowledge of (ρ, η)
Full standard model fit
-1
0
1
-1 0 1 2
sin 2βWA
∆md
∆ms & ∆md
εK
εK
|Vub/Vcb|
ρ
η
CK Mf i t t e r
p a c k a g e
Tree level + CP violating
-1
0
1
-1 0 1 2
sin 2βWA
εK
εK
|Vub/Vcb|
ρ
η
CK Mf i t t e r
p a c k a g e
Z L — SSI p.1/15
Summary — so far
• The CKM picture of CPV passed its first non-trivial test; sin 2β has become thebest known ingredient of the unitarity triangleParadigm change: look for corrections to – rather than alternatives to CKM picture
Questions: Is the SM the only source of CPV?
Questions: Does the SM fully explain flavor physics?
Key measurements: ones that are theoretically clean and experimentally doable
• Heading towards ≤ 10% test of CKM: Our ability to test CKM in B decaysdepends on precision of measurements besides sin 2β and |Vtd/Vts| (today)
Central themes: 1) How to determine |Vub| model independently (2nd lecture)
Central themes: 2) Utility of factorization & SU(3) to determine α/ γ from ratesCentral themes: 2) or “simple” time dependent asymmetries (3rd lecture)
Central themes: 3) “Zero prediction” observables: aCP (Bs → ψφ), adir(B → sγ)
Z L — SSI p.1/16
Mixing and CPV in neutral mesons
Neutral meson mixing
• Two flavor eigenstates, e.g.: |B0〉 = |b d〉, |B0〉 = |b d〉; time evolution satisfies
iddt
(|B0(t)〉|B0(t)〉
)=(M − i
2Γ)( |B0(t)〉|B0(t)〉
)M,Γ are 2× 2 Hermitian matrices; CPT implies M11 = M22 and Γ11 = Γ22
Off-diagonal elements due to box diagrams dom-inated by top quarks⇒ sensitive to high scales
Mass eigenstates are eigenvectors of H:|BL〉 = p|B0〉+ q|B0〉 , |BH〉 = p|B0〉 − q|B0〉
b
d
d
b
t
t
W W
b
d
d
b
W
W
t t
|BH,L(t)〉 = e−(iMH,L+ΓH,L/2)t|BH,L〉 time dependence involves mixing and decay
• In the |Γ12| � |M12| limit, which holds for both Bd,s within and beyond the SM
∆m = 2|M12| , ∆Γ = 2|Γ12| cosφ12 , φ12 = arg(−M12
Γ12
)⇒
NP cannot enhanceBs width difference
Z L — SSI p.1/17
Aside: importance of |Γ12| � |M12|
• New physics in mixing modifies M12; new CPV phases may alter φ ≡ arg(q/p)1
Observing φ different from the SM prediction may be the best hope to find NP
Bd,s: Γ12 �M12, K: M12 ∼ Γ12, D: Γ12 ∼ or > M12
Solving the eigenvalue equation:
– If ∆m� ∆Γ, the CPV phase can be LARGE : φ = arg(M12) +O(Γ212/M
212)
– If ∆Γ� ∆m, the CPV phase is SMALL : φ = O(M212/Γ
212)× sin(2φ12)
• If ∆Γ � ∆m then even if new physics dominates M12, the sensitivity of anyphysical observable to it is suppressed by ∆m/∆Γ
In the D system it is possible that long distance contributions and SU(3) breakingenhance ∆Γ compared to ∆m, this would make looking for NP hard
1Note: arg(q/p) is convention dependent; think of it inD decay as the relative phase between q/p and the phase
of a tree level decay assumed to be real.
Z L — SSI p.1/18
Aside: effective Hamiltonians
• Interactions at high scale (weak or new physics) produce local operators at lowerscales (hadron masses)
Consider, e.g., B0 −B0 mixing:b
d
d
b
t
t
W W
b
d
d
b
W
W
t t⇒ �
�� �
���
��
��
�
�
��
� �
�
� �
��
� ��
�
Q(µ) = (bL γν dL) (bL γν dL)
New physics can modify coefficients and/or induce new operators
Going from operators to observables is equally important
In SM: M12 = (VtbV ∗td)2 G
2F
8π2
M2W
mBS
(m2t
M2W
)ηB bB(µ) 〈B0|Q(µ)|B0〉
what we are after calculable perturbatively nonperturbative
ηB bB(µ) : Resumming αns lnn(mW/µ), where µ ∼ mb, is often very important
〈B0|Q(µ)|B0〉 = 23 m
2B f
2B
BBbB(µ) : Hadronic uncertainties enter here
Z L — SSI p.1/19
Bd,s mixing: |Vtd| and |Vts|
∆mq = 2|M12| = |VtbV ∗tq|2 f2BqBBq︸ ︷︷ ︸↗
×[known factors]
Need from lattice QCD — ratio of q = d, s is easier:
ξ2 ≡f2BsBBs
f2BdBBd
= 1 in SU(3) limit
Lattice QCD: ∼ [1.15(6)]2 “typical lattice average”Chiral logs: ∼ 1.3 (Grinstein et al., ’92)
Recent lattice calculation: ξ = 1.32± 0.1 (Kronfeld&Ryan)
A conservative error of ξ is probably sizable at present
This will soon be the main limitation to extract |Vtd/Vts|
Effects of light quarks need to be reliably controlled
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25
∆ms (ps-1)
Am
plitu
de
data ± 1 σ 95% CL limit 14.9 ps-1
1.645 σ sensitivity 19.3 ps-1
data ± 1.645 σdata ± 1.645 σ (stat only)
World average (prel.)
WA: ∆ms > 15 ps−1
s mixing parameter, xsB0 20 40 60 80 100 120
sse
nsiti
vity
for
x
0
2
4
6
8
10
12
14
16
18
20
Exc
lude
d
CDF
5 Sigma Observation
Sig:Bg = 2:1Sig:Bg = 1:1 (default)Sig:Bg = 1:2
CDF sensitivity
Z L — SSI p.1/20
CPV in mixing
• If CP is conserved then physical states are 1√2
(|B0〉 ± |B0〉), corresponding to|q/p| = 1 and argM12 = arg Γ12∣∣∣∣pq
∣∣∣∣ 6= 1 ⇒ CPV in mixing occurs iff 〈BH|BL〉 = |p|2 − |q|2 6= 0
• Simplest example is decay to “wrong sign” lepton
ASL = Γ[B0(t)→`+X]−Γ[B0(t)→`−X]
Γ[B0(t)→`+X]+Γ[B0(t)→`−X]= 1−|q/p|4
1+|q/p|4 = Im Γ12M12
Has been observed in K decay, not yet in B decay
Calculation of Γ12 has large hadronic uncertaintiesNevertheless interesting to look for new physics:
|Γ12/M12| = O(m2b/m
2W ) model independently
arg(Γ12/M12) = O(m2c/m
2b) in SM, maybe O(1) with NP
-1
0
1
-1 0 1 2
Standard SM fit
Theoreticaluncertainties
ρη
CK Mf i t t e r
(hep-ph/0202010)
Z L — SSI p.1/21
CPV in decay
• Decay amplitudes can, in general, receive many contributions:
Af = 〈f |H|B〉 =∑k
Ak eiδk eiφk Af = 〈f |H|B〉 =
∑k
Ak eiδk e−iφk
“weak phases” φk — complex parameters in Lagrangian (in VCKM in the SM)
“strong phases” δk — on-shell intermediate states rescattering, absorptive parts∣∣∣∣∣AfAf∣∣∣∣∣ 6= 1 ⇒ CPV in decay
Can also occur in charged meson and baryon decays
Requires at least two decay amplitudes with different strong and weak phases:
|A|2 − |A|2 = 4A1A2 sin(δ1 − δ2) sin(φ1 − φ2)
Calculations of Ak and δk have large model dependenceCan be interesting for looking for NP, when SM prediction is small (e.g., in b→ sγ)
Z L — SSI p.1/22
CPV in interference between decay and mixing
• If both B0 and B0 can decay to same final state,there’s another possibility; e.g., if |f〉 is a CP
eigenstate:λfCP =
q
p
AfCPAfCP
= ηfCPq
p
AfCPAfCP
0B
0B
CPf
decaymixing
decay
afCP =Γ[B0(t)→ f ]− Γ[B0(t)→ f ]Γ[B0(t)→ f ] + Γ[B0(t)→ f ]
= −(1− |λf |2) cos(∆mt)− 2 Imλf sin(∆mt)1 + |λf |2
CP is violated either if |λ| 6= 1 due to CPV in mixing and/or decay, or if
|λf | = 1, but Imλf 6= 0 ⇒ CPV in interference
• In such cases (|λf | = 1), CP asymmetry measures phase difference in a theoret-ically clean way
afCP = Imλf sin(∆mt)
In the Bd,s systems |q/p| − 1 < O(10−2), so the question is usually |A/A| ?= 1
Z L — SSI p.1/23
B → ψKS,L — a decay everyone loves
• There are many amplitudes, nevertheless |A/A| − 1 < 10−2
“Tree” (b→ ccs): AT ∼[λ2]VcbV
∗cs
“Penguin”: AP ∼[λ2]VtbV
∗ts f(mt)+
[λ2]VcbV
∗cs f(mc)+
[λ4]VubV
∗us f(mu)
Separation between T and P is scheme and scale dependent!
Rewrite P using unitarity, VtbV ∗ts + VcbV∗cs + VubV
∗us = 0
AP ∼[λ2]VcbV
∗cs︸ ︷︷ ︸ [f(mc)− f(mt)] +
[λ4]VubV
∗us︸ ︷︷ ︸ [f(mu)− f(mt)]
same as Tree phase suppressed by λ2
d
d
d
s
b
Wc
cψ
K
B
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d
d
d
s
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• |A/A| − 1 = O[λ2 × (loop)] ⇒ theoretically very clean
λψKS,L = ∓(V ∗tbVtdVtbV ∗td
)(VcbV
∗cs
V ∗cbVcs
)(VcsV
∗cd
V ∗csVcd
)= ∓e−2iβ ⇒ ImλψKS,L = ± sin 2β
Z L — SSI p.1/24
B → φKS,L — window to NP?
• “Naively” no tree contribution to b→ sss, use unitarity to write penguins:
Penguin: AP ∼[λ2]VcbV
∗cs︸ ︷︷ ︸ [f(mc)−f(mt)]+
[λ4]VubV
∗us︸ ︷︷ ︸ [f(mu)−f(mt)]
dominant contribution suppressed by λ2
Tree: b→ uus followed by uu→ ss rescattering
Constrain rescattering by measuring B+ → φπ+,K∗K+
(Grossman, Isidori, Worah)
ψKS: NP expected to enter λψK mainly through q/p
φKS: NP could enter λφK through both q/p and A/A
s
s
u
u
W
G
bu, c, t
B
s
K
+
+
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u,d
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b qq
s
s
q
q
B π
Κs
s
φ
K
u,d
Expect sin 2βφK = sin 2βψK to hold in the SM at ∼ 5% level
• Measuring same angle in decays sensitive to different short distance physics isimportant! [See also the data for η′KS and K+K−KS]
Z L — SSI p.1/25
Summary
• Seeking experimentally precise and theoretically reliable measurements that inthe SM relate to CKM elements but can probe different short distance physics
• The CKM picture passed its first nontrivial test; we can no longer claim to belooking for alternatives of CKM, but to seek corrections due to new physics(Except maybe Bs system, Imλsss, ...)
• Very broad program — a lot more interesting as a whole than any single mea-surement alone; redundancy / correlations may be the key to new physics
• Bd,s mixing (|Vtd/Vts|) and B → ψK (sin 2β) are “easy”(i.e., both theory and experiment under control)
• Tomorrow we’ll start looking at harder things...
Z L — SSI p.1/26
Second Lecture
• Heavy quark symmetry
... Spectroscopy with HQS
• Exclusive semileptonic decays
... B → D(∗)`ν decays and |Vcb|
... Heavy to light decays
• Inclusive semileptonic decays
... B → Xc`ν and |Vcb|
... Inclusive |Vub| measurements and rare decays
• Summary
• Additional topics... B decays to excited D mesons; exclusive & inclusive rare decays
Preliminaries
• Theoretical tools to analyze semileptonic and rare decays are similar
Allow measurements of CKM elements and are sensitive to new physics
Improved understanding of hadronic physics and accuracy of theoretical predic-tions affects sensitivity to new physics
• For the purposes of this and tomorrow’s talks, [strong interaction] model indepen-dent ≡ theoretical uncertainty suppressed by small parameters
Most of the recent progress comes from expanding in powers of Λ/mQ, αs(mQ)... a priori not known whether Λ ∼ 200MeV or ∼ 2GeV (fπ,mρ,m
2K/ms)
... need experimental guidance to see which cases work how well
Z L — SSI p.2/1
Heavy quark symmetry
QQ : positronium-type bound state, perturbative in mQ � ΛQCD limit
Qq : wave function of the light degrees of freedomQq : (“brown muck”) insensitive to spin and flavor of Q
B meson is a lot more complicated than just a b q pair
In the mQ → ∞ limit, the heavy quark acts as a staticcolor source with fixed four-velocity vµ
⇒ SU(2n) heavy quark spin-flavor symmetry at fixed vµ
1/mQ
1/ΛQCD
Similar to atomic physics (me � mN):
1. Flavor symmetry ∼ isotopes have similar chemistry [Ψe independent of mN ]
2. Spin symmetry∼ hyperfine levels almost degenerate [~se−~sN interaction→ 0]
Z L — SSI p.2/2
Spectroscopy of heavy-light mesons
• In mQ → ∞ limit, spin of the heavy quark is a good quantum number, and so isthe spin of the light d.o.f., since ~J = ~sQ + ~sl and
angular momentum conservation: [ ~J,H] = 0heavy quark symmetry: [~sQ,H] = 0
}⇒ [~sl,H] = 0
For a given sl, two degenerate states:
J± = sl ± 12
⇒ ∆i = O(ΛQCD) — same in B and D sector
Doublets are split by order Λ2QCD/mQ, e.g.:
mD∗ −mD ' 140 MeVmB∗ −mB ' 45 MeV
∆3
∆2
∆1
∆3mb −mc
∆2
∆1
32
+(B1, B
∗2)
12
+(B∗1, B
∗0)
12
−(B,B∗)
32
+(D1, D
∗2)
12
+(D∗1, D
∗0)
12
−(D,D∗)
Z L — SSI p.2/3
Aside: a puzzle
Since vector–pseudoscalar mass splitting ∝ 1/mQ, expect: m2V −m2
P = const.
This argument relies on mQ � ΛQCD
Experimentally: m2B∗ −m2
B = 0.49 GeV2
Experimentally: m2B∗s−m2
Bs= 0.50 GeV2
Experimentally: m2D∗ −m2
D = 0.54 GeV2
Experimentally: m2D∗s−m2
Ds= 0.58 GeV2
Experimentally: m2ρ −m2
π = 0.57 GeV2
Experimentally: m2K∗ −m2
K = 0.55 GeV2
Not understood... there is something more going on than just HQS!
Z L — SSI p.2/4
Charmed meson spectrum
(hep-ex/9908009)
“Successes:”
D1 is narrow: S-wave D1 → D∗ π
amplitude allowed by angularmomentum conservation, butforbidden in the mQ → ∞ limit byheavy quark spin symmetry
Mass splittings of orbitally excitedstates is small:mD∗2−mD1 = 37 MeV� mD∗−mD
vanishes in the quark model, sinceit arise from 〈~sQ · ~sq δ3(~r )〉
Z L — SSI p.2/5
Aside: strong decays of D1 and D∗2
• The strong interaction Hamiltonian conserves the spin of the heavy quark and thelight degrees of freedom separately
(D1, D∗2)→ (D,D∗)π — four amplitudes related by heavy quark spin symmetry
Γ(j → j′ π) ∝ (2sl + 1)(2j′ + 1)∣∣∣∣{L s′l sl
12 j j′
}∣∣∣∣2Multiplets have opposite parity ⇒ π must be in L = 2 partial wave
Γ(D1 → Dπ) : Γ(D1 → D∗π) : Γ(D∗2 → Dπ) : Γ(D∗2 → D∗π)
0 : 1 : 25 : 3
5
0 : 1 : 2.3 : 0.92
• Last line includes large |pπ|5 HQS violation from phase space, which changesΓ(D∗2 → Dπ)/Γ(D∗2 → D∗π) from 2/3 to 2.5 (data: 2.3± 0.6)
[Note: prediction for ratio of D1 and D∗2 total widths works less well (Falk & Mehen)]
Z L — SSI p.2/6
Semileptonic and rare B decays
|Vub| is the dominant uncertainty ofthe side of the UT opposite to β = φ1
Error of |Vcb| is a large part of theuncertainty in the εK constraint, andin K → πνν when it’s measured 0
0.2
0.4
0.6
0.8
1
-1 -0.5 0 0.5 1
sin 2βJ/ΨKs
∆md ∆ms & ∆md
εK
εK
|Vub/Vcb|
ρη
C K Mf i t t e r
p a c k a g e
|Vcb|4
Vub
Rare decays mediated by b → sγ, b → s `+`−, and b → s νν transitions aresensitive probes of the Standard Model
Exclusive B → D(∗)`ν decay
• In the mb,c → ∞ limit, configuration of brown muck only depends on the four-velocity of the heavy quark, but not on its mass and spin
Weak current changes b→ c, i.e.:
~pb → ~pc and possibly flips ~sQ, on a time scale� Λ−1QCD
In mb,c � ΛQCD limit brown muck only feels vb → vc
Form factors independent of Dirac structure of weakcurrent ⇒ all form factors related to a single functionof w = v · v′, the Isgur-Wise function, ξ(w)︸︷︷︸
⇑
ν
�����
Contains all nonperturbative low-energy hadronic physics
• ξ(1) = 1, because at “zero recoil” configuration of brown muck not changed at all
Z L — SSI p.2/7
B → D(∗)`ν form factors
• Lorentz invariance ⇒ 6 form factors
〈D(v′)|Vν|B(v)〉 =√mBmD
[h+ (v + v′)ν + h− (v − v′)ν
]〈D∗(v′)|Vν|B(v)〉 = i
√mBmD∗ hV εναβγε
∗αv′βvγ
〈D(v′)|Aν|B(v)〉 = 0
〈D∗(v′)|Aν|B(v)〉 =√mBmD∗
[hA1 (w + 1)ε∗ν − hA2 (ε∗ · v)vν − hA3 (ε∗ · v)v′ν
]Vν = cγνb, Aν = cγνγ5b, w ≡ v · v′ = m2
B +m2D − q2
2mBmD, and hi = hi(w, µ)
• In mQ →∞ limit, up to corrections suppressed by αs and ΛQCD/mc,b
h− = hA2 = 0 , h+ = hV = hA1 = hA3 = ξ(w)
αs corrections calculableΛQCD/mc,b corrections is where model dependence enters
Z L — SSI p.2/8
|Vcb| from B → D(∗)`ν
• Extract |Vcb| from w ≡ v · v′ = m2B+m2
D−q2
2mBmD= 1 limit of B → D(∗)`ν rate
dΓ(B → D(∗)`ν)dw
= (known factors) |Vcb|2F2(∗)(w)
F(∗)(w) = Isgur-Wise function +O(αs,ΛQCD/mc,b)
F(1) = 1Isgur−Wise + 0.02αs,α2s
+(lattice or models)
mc,b+ . . .
F∗(1) = 1Isgur−Wise − 0.04αs,α2s
+0Luke
mc,b+
(lattice or models)m2c,b
+ . . .
ν
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⇒ theorists argue about small corrections
Near zero recoil: dΓ/dw ∝{√
w2 − 1 for B → D∗
(w2 − 1)3/2 for B → D (helicity!)
B → D∗ preferred both experimentally and theoretically (except lattice QCD)
Z L — SSI p.2/9
Experimental status of |Vcb|exclusive
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
1 1.1 1.2 1.3 1.4 1.5
Fit
● Data
y
|Vcb
|F(y
)
Functional form used to extrapolate to zero recoil isvery important — shape related to B → D∗∗`ν decay
Experiments measure: |Vcb| F∗(1)
Theory predicts: F∗(1) = 0.91± 0.04
⇒ |Vcb| = (41.9± 1.1± 1.9)× 10−3 (Battaglia @ ICHEP)
B → D`ν may be important:
Difference of slopes is anorder ΛQCD/mc,b effect...
Corellation between slopeand |Vcb| very large
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
28 30 32 34 36 38 40 42 44 46
ALEPH.
DELPHI .OPAL
.
CLEO.
Belle
.ρ∗
2�
|Vcb | F*(1)× 10 3�
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
2.5 3 3.5 4 4.5 5
|Vcb | F(1)× 102
ρ2
ALEPH 1997
CLEO 1997
CLEO 1999
BELLE 2001
B → D∗`ν B → D`ν
Z L — SSI p.2/10
Uncertainties in |Vcb|exclusive
• Nonperturbative correction at zero recoil
– Bounds from sum rules or models2
– Lattice QCD: Calculate F(∗) − 1 from a double ratio of correlation functions
F(1) = 1.06± 0.02 , F∗(1) = 0.91± 0.03, D not harder than D∗ (FNAL, quenched)
Checks: consistency between B → D∗ and D, and the form factor ratios (R1,2)
• Extrapolation to zero recoil
– Unitarity constraints: strong correlation between slope & curvature of F(∗)(w)(Boyd, Grinstein, Lebed; Caprini, Lellouch, Neubert)
– Constrain slopes by studying decays to excited D∗∗, B → D∗∗`ν, near w = 12“When you have to descend into the brown muck, you abandon all pretense of doing elegant, pristine, first-
principles calculations. You have to get your hands dirty with uncontrolled approximations and models. When you
are finished with the brown muck you should wash your hands.” (H. Georgi, TASI’ 1991)
Z L — SSI p.2/11
B → light form factors
• Limited use of HQS: relateB → ρ`ν, K∗`+`−, K∗γ form factors in large q2 region,but HQS neither reduces number of form factors, nor determines their normaliza-tion at any value of q2
BuΓb Vub−−−−→ ρ `ν
flavorSU(2) l l chiral
SU(3)
DdΓc Vcs−−−−→ K∗`ν
⇒ relations at same v · v′
Can predict B → ρ`ν rate from measured D → K∗`ν form factors
• Corrections to heavy quark symmetry and chiral symmetry could be ∼ 20% each(First order corrections can be eliminated — complicated)
Large q2 region is also what’s most accessible to lattice QCD
Z L — SSI p.2/12
Soft-collinear effective theory
• Recently proposed: for q2 � m2B, 7 vector meson form factors (V,A, T currents)
related to 2 functions; 3 pseudoscalar form factors related to just 1 (Charles et al.)
SCET: a new effective field theory for energetic particles (simplify power counting,helps to make all-order proofs, etc.) (Bauer, Fleming, Luke, Pirjol, Stewart)
Systematic framework to describe form factors when light hadron is very energetic
soft part hard part
extra symmetries calculable corrections
Consistency of separation only proven to 1-loop yet (Beneke & Feldman)
(In B → D(∗)`ν, nonperturbative part is in Isgur-Wise function to all orders)
... Expect progress!
Z L — SSI p.2/13
Aside: an application
• The hope is to use some measurements in a theoretically controlled way to predictother decay rates; e.g., use B → K∗γ data to reduce uncertainty of B → K∗`+`−
and B → ρ`ν predictions, and also constrain models
Perturbative order αs corrections have been computed (Beneke, Feldman, Seidel)
(Burdman & Hiller)
Crucial questions: all orders proof and understand power suppressed corrections
Z L — SSI p.2/14
Exclusive decays — Summary
• Heavy quark symmetry provides many model independent predictions, similar tochiral symmetry
Spectroscopy, strong and weak decays much better understood
• B → D(∗)`ν: six semileptonic form factors depend on a single Isgur-Wise functionin the mQ →∞ limit; at zero recoil ξ(1) = 1, sometimes no ΛQCD/mQ corrections
|Vcb| known at∼ 5% level from exclusive decays (improvements will rely on lattice)
• Progress to understand exclusive heavy→ light semileptonic and rare decays forsmall q2; SCET might lead to rigorously proving
Form factor relations between B → π`ν, B → ρ`ν, B → K∗γ, B → K(∗)`+`−
– increase sensitivity to new physics– tests some assumptions for factorization in charmless decays (more tomorrow)
Z L — SSI p.2/15
Inclusive decays
Operator product expansion
• Consider semileptonic b→ c decay: Obc = −4GF√2Vcb (c γµPL b)︸ ︷︷ ︸
Jµbc
(` γµPL ν)︸ ︷︷ ︸J`µ
Decay rate: Γ(B → Xc`ν) ∼∑Xc
∫d[PS]
∣∣〈Xc`ν|Obc|B〉∣∣2
Factor to: B → XcW∗ and W ∗ → `ν, concentrate on hadronic part
Wµν ∼∑Xc
δ4(pB − q − pX)∣∣〈B|Jµ†bc |Xc〉 〈Xc|Jνbc|B〉
∣∣2(optical theorem) ∼ Im
∫dx e−iq·x 〈B|T
{Jµ†bc (x) Jνbc(0)
}|B〉
In mb � ΛQCD limit, time ordered product dominated by x� Λ−1QCD
b b
p =mv+k
q q
p =mv-q+kq
b
=�
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Z L — SSI p.2/16
OPE (cont.)
• The mb →∞ limit is given by free quark decay
No O(ΛQCD/mb) corrections
Order Λ2QCD/m
2b corrections depend on two hadronic matrix elements
λ1 =1
2mB〈B| b (iD)2 b |B〉 λ2 =
16mB
〈B| b g2σµν G
µν b |B〉
not well-known λ2 = (m2B∗ −m2
B)/4
• OPE predicts decay rates in an expansion in ΛQCD/mb and αs(mb)
dΓ =(b quarkdecay
)×{
1 +0mb
+f(λ1, λ2)m2b
+ . . .+ αs(. . .) + α2s(. . .) + . . .
}Interesting quantities computed to order αs, α2
sβ0, and 1/m3
When can we trust the result?
Z L — SSI p.2/17
Inclusive decay rates
• In which regions of phase space can we expect the OPE to converge?
b b
p =mv+k
q q
p =mv-q+kq
b
Can think of the OPE as an expansion in k ∼ ΛQCD
[(mbv + k − q)2 −m2q]−1
= [(mbv − q)2 −m2q + 2k · (mbv − q) + k2]−1
Need to allow: m2X −m2
q � EXΛQCD � Λ2QCD
Implicit assumption: “quark-hadron duality” valid once mX � mq allowed
• Good news: Total rates calculable at few (<∼ 5) percent level (duality...) ⇒ |Vcb|
Need to know mb (or Λ = mB −mb) and λ1
|Vcb| ∼[42± (error mostly in mb &λ1)
]× 10−3
(B(B → Xc`ν)
0.1051.6 psτB
)1/2
• Bad news: In certain restricted regions of phase space the OPE breaks down
To determine |Vub|, cuts required to eliminate∼100 times larger b→ c background
Z L — SSI p.2/18
Determination of mb & λ1⇒ |Vcb|
• Progress likely to come from determining mb and λ1 from “shape variables” ininclusive B decays ∼ 〈Enγ 〉 in B → Xsγ, 〈En` 〉 and 〈mn
Xc〉 in B → Xc`ν
These have been computed to α2sβ0 and (ΛQCD/mQ)3
CLEO:
Λ = 0.35± 0.13 GeVλ1 = −0.24± 0.11 GeV2
⇓|Vcb| ∼ (40.4± 1.6)× 10−3
γ
λ �
Λ
(CLEO)
M1(
MX
) (G
eV)
E l cut (GeV)
DELPHI preliminary( Λ , λ1 , Τ )
(0.39,−0.25,−0.2)(0.39,−0.25, 0.0)
( Λ , λ1 , Τ )(0.35,−0.17, 0.0)
(Babar, Delphi)
Level of (in)consistency will test accuracy of OPE and quark-hadron duality
⇒ May lead to σ(Vcb) ∼ 2− 3% if all works out
Z L — SSI p.2/19
Inclusive b→ u : the problem
dΓ(b→c)/dEe
10 dΓ(b→u)/dEe
Ee (GeV)
dΓ/d
Ee
∆E
0
20
40
60
80
0 1 2(hep-ph/0011181)
|Vub| ∼1
10|Vcb| ⇒ cuts
... and the troubles begin
Z L — SSI p.2/20
Inclusive B → Xu`ν decay and |Vub|
Proposals to measure |Vub|:
– Lepton spectrum: E` > (m2B −m2
D)/2mB
– Hadronic mass spectrum: mX < mD
– Dilepton mass spectrum: q2 > (mB −mD)2
ν
��
0.5 1 1.5 2�
5
10
15
20
25
Ee (GeV)
q2 (GeV� 2)
b→c allowed Ee>(mB-mD)/2mB
2 2
q� 2>(mB-mD)2
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5 10 15 20�
25
5
10
15
20
25
q2 (GeV� 2)
mX (GeV2)2
b→c allowed
m� X< mD
q� 2>(mB-mD)2
� �� �
O Otheory⇐=breaks =⇒
down
Z L — SSI p.2/21
B → Xu`ν spectra
• Three qualitatively different regions of phase space:
1) m2X � EXΛQCD � Λ2
QCD: the OPE converges, first few terms can be trusted
2) m2X ∼ EXΛQCD � Λ2
QCD: infinite set of terms in the OPE equally important
3) mX ∼ ΛQCD: resonance region — cannot compute reliably
• Problem: E` > (m2B−m2
D)/2mB and mX < mD are in (2) since mBΛQCD ∼ m2D
0�
.5 1 1.5 2
0.2
0.4
0.6
0.8
2�
.5
El (GeV)
ΓdΓ
dEl
_1 __dmXΓ
_1 dΓ__
1 2 3 4 5�
6
0.2
0.4
0.6
0.8
1
mX (GeV )2�2
2
(GeV-1)
(GeV-2)
q2 (GeV )2�
ΓdΓdq2
_1 __
5�
10 15 20 25
0�
.02
0�
.04
0�
.06
0�
.08
(GeV-2)
b→ c b→ c b→ c
−− b quark decay to O(αs)−− incl. “Fermi-motion” (model)
Experiment happy
Theory happy
Z L — SSI p.2/22
Vub: lepton endpoint region
• Bad: an infinite set of terms in the OPE are equally importantGood: it is related to B → Xsγ photon spectrum (Neubert; Bigi, Shifman, Uraltsev, Vainshtein)
Recently: Perturbative corrections worked out to higher order (Leibovich, Low, Rothstein)
Recently: Terms in the OPE not related to B → Xsγ are also significant(Leibovich, ZL, Wise; Bauer, Luke, Mannel)
CLEO used the B → Xsγ photon spectrum as an inputto determine |Vub|... measures the “Fermi-motion” of the b quark
|Vub| = (4.08± 0.63)× 10−3
Limiting uncertainties: subleading correctionsLimiting uncertainties: quark-hadron duality applicable?
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������� ��������������� ��� "!$#�%�&�' � ��(�) *+ ! #-,�' � ��(.)
(CLEO)
Z L — SSI p.2/23
Vub: q2 spectrum
• In large q2 region, first few terms in OPE can be trusted (Bauer, ZL, Luke)
Reason: q2 > (mB −mD)2 cut implies EX < mD, therefore m2X � EXΛQCD
Some nonperturbative corrections are (ΛQCD/mc)3, and not (ΛQCD/mb)3 (Neubert)
Possibly sizable corrections at O(ΛQCD/mb)3
from weak annihilation (Voloshin)
Guesstimate: ∼ 2–3% ofb → u semileptonic rate;delta-function at maximalq2 and maximal E`
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8�
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0 1�
2 1�
40�
0�
.1
0�
.2
0�
.3
0�
.4
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.5
WA
o� ther O(Λ/mb)3
q� 2 (GeV2)cut
∆�
GG
error in rate as a function of q2
Comparing D0 vs. Ds SL widths, or Vub from B± vs. B0 decay can constrain WA
Z L — SSI p.2/24
Vub: combine q2 & mX cuts
• Can get |Vub| with theoretical uncertainty at the 5–10% level, from up to ∼ 45% ofthe events (Bauer, ZL, Luke)
Such precision can be achieved even with cuts away from the b→ c threshold
Cuts on (q2, mX)included fractionof b→ u`ν rate
error of |Vub|δmb = 80/30 MeV
6 GeV2, mD 46% 8%/5%8 GeV2, 1.7 GeV 33% 9%/6%(mB −mD)2,mD 17% 15%/12%
Strategy: (i) reconstruct q2 and mX; make cut on mX as large as possibleStrategy: (ii) for a given mX cut, reduce q2 cut to minimize overall uncertainty
... Would significantly reduce the uncertainty of a side of the unitarity triangle
Z L — SSI p.2/25
Semileptonic & rare decays — Summary
• |Vcb| is known at the ∼ 5% level; error may become half of this in the next fewyears using both inclusive and exclusive determinations (latter will rely on lattice)
• Situation for |Vub| may become similar to present |Vcb|; for precise inclusive deter-mination the neutrino reconstruction seems crucial; the exclusive will use lattice
• For both |Vcb| and |Vub| it is important to pursue both inclusive and exclusive
• Progress in understanding exclusive rare decays for q2 � m2B (expect more!)
B → K(∗)γ and B → K(∗)`+`− below the ψ⇒ increase sensitivity to new physics
Related to some issues in factorization in charmless decays (tomorrow)
Z L — SSI p.2/26
Additional Topics
• B decays to excited D mesons
• Exclusive rare decays
• Inclusive rare decays
Decays to excited states: B → D∗∗`ν
• HQS⇒ matrix elements of weak currents vanish at zero recoil for excited statesBecome non-zero at O(ΛQCD/mQ) — most of the phase space is near zero recoil
mQ →∞: for each doublet, all form factors are related to an Isgur-Wise function
O(ΛQCD/mQ): in B → (D1, D∗2)`ν, 8 subleading I-W fn’s, but only 2 independent
dΓ(B → D1`ν)dw
∝√w2 − 1 [τ(1)]2
{0 + 0 (w − 1) + (. . .)(w − 1)2 + . . .
+ΛQCD
mQ
[0 + (almost calculable)(w − 1) + . . .
]+
Λ2QCD
m2Q
[(calculable!) + . . .
]+ . . .
}w ≡m2B+m2
D1−q2
2mBmD1∈ (1, 1.3)
In B → (orbitally excited D) decays, the zero recoil matrix element at O(1/mQ)is given by mass splittings and the mQ →∞ Isgur-Wise fn. (Leibovich, ZL, Stewart, Wise)
Z L — SSI p.2/27
More B → D∗∗`ν
• Bjorken sum rule for the slope of Isgur-Wise function (∃ many more sum rules):
ρ2 =14
+∑m
|ζ(m)(1)|2
4+ 2
∑p
|τ (p)(1)|2
3+ nonresonant
ζ(m) and τ (p) are Isgur-Wise fn’s for the 12
+and 3
2
+states
B → D1`ν rate is enhanced at order ΛQCD/mQ bymuch more than D∗2`ν
The present world average is about 0.4± 0.15
Approximation ΓD∗2/ΓD1
mQ →∞ 1.65
Finite mQ
{B1
B2
0.52
0.67
• To compare B → (D1, D∗2) with (D∗0, D
∗1), need to know the Isgur-Wise functions
Quark models (ISGW, etc.) and QCD sum rules predict that the Isgur-Wise func-tion for the broad doublet is not larger than for the narrow doublet
If you buy these arguments, then the large B → (D∗0, D∗1)`ν rate is a puzzle
Z L — SSI p.2/28
B → D∗∗π decays
• Factorization is expected to work as well as in B → D(∗)π
Γπ =3π2 |Vud|2C2 f2
π
m2B r
×(
dΓsl
dw
)wmax
r = mD∗∗/mB , wmax = (1 + r2)/(2r) ' 1.3 , fπ ' 132 MeV , C |Vud| ' 1
• An interesting ratio from which Isgur-Wise function cancels out:
B(B− → D∗02 π−)
B(B− → D01π−)
= 0.89± 0.14 (BELLE @ ICHEP)
This looks OK and can teach us about 1/m corrections (in ’97 ratio was 1.8± 0.9,theory could not accommodate such a large central value) (Leibovich, ZL, Stewart, Wise)
Sorting out these semileptonic and nonleptonic decays to excited D’s will beimportant for HQET, factorization, and will impact |Vcb| determinations
Z L — SSI p.2/29
Exclusive rare decays
• Important probes of NP — measurements of |Vij|
Exclusive decays are experimentally easier — need to understand form factors
– B → K∗γ or B → Xsγ: best mH± limits in 2HDM — in SUSY many param’s
– B → K(∗)`+`− or B → X `+`−: bsZ penguins, SUSY, right handed couplings
• There is an observable insensitive to the precise values of the form factors:
model insensitive (Burdman) Forward-backward asymmetry in B → K∗`+`−
changes sign:
Ceff9 (s0) = −2mBmb
s0Ceff
7 × [ 1 +O(αs,ΛQCD/mb)]
O(αs) corrections computed (Beneke, Feldman, Seidel)
May give clean measurement of C9 (sensitive to NP)
Z L — SSI p.2/30
B → K∗γ briefly
Large (∼ 80%) enhancement of B → K∗γ decayrate found at NLO
⇒ 1/m correction large or/and form factors sig-nificantly different from model predictions
2 3 4 5 6 7 8 9
0.05
0.1
0.15
0.2
0.25
�
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(Beneke, Feldmann, Seidel; Bosch, Buchalla)
Form factors also enter predictions for isospin splitting — power suppressed cor-rection, but claimed to be calculable
∆0− = Γ(B0→K∗0γ)−Γ(B−→K∗−γ)
Γ(B0→K∗0γ)+Γ(B−→K∗−γ)= 0.02± 0.07 (data)
∆0− = (0.08+2.1−3.2)%× 0.3
TB→K∗
1
(Kagan & Neubert)
Testing these predictions may be important for understanding various approachesto factorization in charmless decays
Z L — SSI p.2/31
Inclusive rare B decays
• Important probes of new physics — measurements of CKM elements
– B → K∗γ or Xsγ: Best mH± limits in 2HDM — in SUSY many param’s
– B → K(∗)`+`− or Xs`+`−: bsZ penguins, SUSY, right handed couplings
A crude guide... (` = e or µ)Decay ∼SM rate physics examples
B → sγ 3× 10−4 |Vts|, H±, SUSY
B → sνν 4× 10−5 new physics
B → τν 4× 10−5 fB|Vub|, H±
B → s`+`− 7× 10−6 new physics
Bs → τ+τ− 1× 10−6
B → sτ+τ− 5× 10−7 ...
B → µν 3× 10−7
Bs → µ+µ− 4× 10−9
B → µ+µ− 1× 10−10
Replacing b → s by b → d costsfactor ∼20 (in SM)
In B → q l1 l2 decays expect∼10–20% K∗/ρ, and ∼5–10% K/π
(model dependent)
So far the b → s`+`− data agreeswith the SM expectation within thestill sizable errors
Z L — SSI p.2/32
Something to worry about?
B(B → ψXs) ∼ 4× 10−3
↓B(ψ → `+`−) ∼ 6× 10−2
So this “long distance” contribution is:
B(B → Xs`+`−) ∼ 2× 10−4
This is ∼ 30 times the short distance contribution! �
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Averaged over a large region of invariant masses (and 0 < q2 < m2B should be
large enough), the cc loop expected to be dual to ψ+ψ′+. . . This is what happensin e+e− → hadrons, in τ decay, etc., but NOT here
Is it consistent to “cut out” the ψ and ψ′ regions and then compare data with theshort distance calculation? (Maybe..., but understanding is unsatisfactory)
Z L — SSI p.2/33
Third Lecture
• Clean determination of angles
... Bs → DsK or B → D(∗)π
... B → ππ with isospin analysis, etc.
• Factorization in B → D(∗)X decay
... How / why to test it
• Factorization in charmless decays
... different approaches
... some predictions / applications
• Summary / Conclusions
Angles — cleanly
B → ψKS,L — saw this before
• Clean measurement possible because |λψKS,L| − 1� 1
afCP =Γ[B0(t)→ f ]− Γ[B0(t)→ f ]Γ[B0(t)→ f ] + Γ[B0(t)→ f ]
= Sf sin(∆mt)− Cf cos(∆mt)
λfCP = qp
AfCPAfCP
= ηfCPqp
AfCP
AfCP, Sf = 2Imλf
1+|λf |2, Cf = 1−|λf |2
1+|λf |2
Tree: AT ∼ VcbV∗cs
Penguin: AP ∼[λ2]VtbV
∗ts f(mt) +
[λ2]VcbV
∗cs f(mc) +
[λ4]VubV
∗us f(mu)
= VcbV∗cs︸ ︷︷ ︸ [f(mc)−f(mt)]+VubV ∗us︸ ︷︷ ︸ [f(mu)−f(mt)]
same as Tree phase suppressed by λ2
d
d
d
s
b
Wc
cψ
K
B
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d
d
d
s
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b
ψ
Wu,c,t
c
c
K
B
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λψKS,L = ∓(V ∗tbVtdVtbV ∗td
)(VcbV
∗cs
V ∗cbVcs
)(VcsV
∗cd
V ∗csVcd
)= ∓e−2iβ ⇒ ImλψKS,L = ± sin 2β
Z L — SSI p.3/1
Bs→ ψφ and Bs→ ψη(′)
• Analog of B → ψKS in Bs decay — determines the phase between Bs mixingand b→ ccs decay, βs, as cleanly as the determination of β
βs is a small angle (of order λ2) inone of the “squashed” UT’s
0
0.25
0.5
0.75
1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
Without aψKWith aψK
sin2βS
CL
CK Mf i t t e r
(hep-ph/0202010)
• ψφ is a VV final state, so the asymmetry will be diluted by the CP -odd component⇒ A large asymmetry would clearly signal NP
ψη(′), on the other hand, is pure CP -even
Z L — SSI p.3/2
B → ππ — the problem
• There are tree and penguin amplitudes, just like for ψKS
“Tree” (b→ uud): AT ∼[λ3]
VubV∗ud
“Penguin”: AP ∼[λ3]VtbV
∗td f(mt)+
[λ3]VcbV
∗cd f(mc)+
[λ3]VubV
∗ud f(mu)
(unitarity) ∼[λ3]
VubV∗ud︸ ︷︷ ︸ [f(mu)− f(mt)] +
[λ3]VcbV
∗cd︸ ︷︷ ︸ [f(mc)− f(mt)]
same as Tree phase not suppressed
Two amplitudes with different weak- and possibly differentstrong phases; their values not known model independently
d
d
W
B
u
u
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-
d
b
π
π
+
d
d
d
d
W
G
bu, c, t
Bu
u
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π
-π
+
Define P and T by: Aπ+π− = T (VubV ∗ud) + P (VcbV ∗cd)
Ratio of Kπ and ππ rates indicates |P/T | ∼ 0.2− 0.4, i.e., |P/T | 6� 1
• Possible solutions: (1) eliminate P ; or (2) attempt to calculate P
Z L — SSI p.3/3
B → ππ — isospin analysis
(u, d): I-spin doublet
other quarks and gluons: I = 0
γ, Z: mixtures of I = 0, 1
(ππ)`=0 → If = 0 or If = 2(1× 1) (∆I = 1
2) (∆I = 32)
I = 0 final state forbidden by Bose symmetry
Hamiltonian has two parts: ∆I = 12 ⇒ If = 0
Hamiltonian has two parts: ∆I = 32 ⇒ If = 2 ... only two amplitudes
3 rates: B0 → π+π−, B0 → π0π0, and B− → π0π− determine magnitudes andrelative phase of two amplitudes ... similarly for B0 and B+ decay
In practice, need all (tagged) rates + time dependent asymmetry in B → π+π−
Note: γ and Z penguins violate isospin and yield some (small) uncertainty
Z L — SSI p.3/4
Isospin analysis (cont.)
A+− ≡ A(B0 → π+π−), A+− ≡ A(B0 → π+π−),A00 ≡ A(B0 → π0π0), A00 ≡ A(B0 → π0π0),A+0 ≡ A(B+ → π+π0), A−0 ≡ A(B− → π−π0).
Isospin symmetry implies that 6 amplitudesform two triangles with a common base
1√2A+−+A00 = A+0,
1√2A+−+A00 = A−0
|A+0| = |A−0|
2δ = difference between arg λπ+π− and 2α
(constrained by any limit on π0π0 rate – later)
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(hep-ph/9712306)
B → ρπ: 4 isospin amplitudes⇒ pentagon relationsB → ρπ: Dalitz plot analysis would allow considering π+π−π0 final state only
Z L — SSI p.3/5
Implications of current data
• Babar and Belle measured:
Sπ+π− =2 Imλππ
1 + |λππ|2≡ sin 2αeff , Cπ+π− =
1− |λππ|2
1 + |λππ|2
λππ = e−2iβ e−iγ + P/T
eiγ + P/T
If P/T were small, then |λππ| ' 1 and Sπ+π− = Imλππ ' − sin 2(β + γ) = sin 2α
Cπ+π− measures: |λππ|2 =1− Cπ+π−
1 + Cπ+π−(note: S2 + C2 ≤ 1, and = 1 iff Reλ = 0)
Central values of Cπ+π− imply Babar: −0.30± 0.25± 0.04 ⇒ modest P/T
Central values of Cπ+π− imply Belle: −0.94+0.31−0.25 ± 0.09 ⇒ large P/T
• To extract α from Sπ+π− alone, need to know magnitude and phase of P/T
Z L — SSI p.3/6
Implications for P/T — another way
Assume the SM is correct, use Sππ and Cππ measurements to constrain magni-tude and phase of P/T (≡ zππ eiφππ)
0
60
120
180
240
300
360
0 0.5 1 1.5 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GR �
[2001]�
BBNS [2001]�
Constraint from SM(ρ,η� ) and Sππ, Cππ (BABAR) confidence level�
zπ� π�
φ ππ
(d
egre
es)
CK Mf i t t e r
0
60
120
180
240
300
360
0 0.5 1 1.5 20
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
GR �
[2001]�
BBNS [2001]�
Constraint from SM(ρ,η� ) and Sππ, Cππ (Belle) confidence level�
zπ� π�
φ ππ
(d
egre
es)
CK Mf i t t e r
(Hocker @ FPCP)
need more data...
Z L — SSI p.3/7
Bounding α− αeff
0
50
100
150
0 50 100 1500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Standard SM fit
α (deg)
α eff
(de
g)
Constraint from GL isospin analysis (BABAR) confidence level�
CK Mf i t t e r
R&�
D
Isospin relations + branching ratios + limit on B → π0π0 ⇒ bound on α− αeff
No strong constraint from present bound on B → π0π0
Z L — SSI p.3/8
Bs→ D±s K∓ — a different story
• Interference between Bs and Bs decay — only one tree amplitude in each case
Four amplitudes: BsA1→ D+
s K− (b→ cus) , Bs
A2→ K+D−s (b→ ucs)
Four amplitudes: BsA1→ D−s K
+ (b→ cus) , BsA2→ K−D+
s (b→ ucs)
AD+s K−
AD+s K−
=A1
A2
(VcbV
∗us
V ∗ubVcs
),
AD−s K+
AD−s K+
=A2
A1
(VubV
∗cs
V ∗cbVus
)Relative strong phase and magnitudes of A1 and A2 are unknown, still theoryerror is eliminated if four time dependent rates are measured:
λD+s K−
λD−s K+ =(V ∗tbVtsVtbV ∗ts
)2(VcbV
∗us
V ∗ubVcs
)(VubV
∗cs
V ∗cbVus
)= e−2i(γ−2βs−βK)
• Similarly, Bd → D(∗)±π∓ determines γ + 2β: λD+π− λD−π+ = e−2i(γ+2β)
... ratio of amplitudes O(λ2)⇒ expected asymmetries are small
Z L — SSI p.3/9
B±→ (D0, D0)K±→ fiK±
• B± → K±D: theoretically clean, experimentally very hard (Gronau-Wyler)
|A(B+ → K+D0)||A(B+ → K+D0|
∼ λ
Nc
• B± → K±(D0, D0)→ K±fi (i = 1, 2) (Atwood, Dunietz, Soni)
make use of large final state interaction in D decay
Idea: B+ → K+D0 → K+fi in doubly Cabibbo suppressed D0 decay
Idea: B+ → K+D0 → K+fi in Cabibbo allowed D0 decay (e.g.: fi = K−π+/ρ+)
Need at least 2 final states Total Br’s ∼ 10−7 — statistics?
• Many ideas on the market would become a lot simpler if some of the hadronicdecay amplitudes were understood
Z L — SSI p.3/10
Factorization in b→ c
Factorization in b→ c exclusive decays
B D
πStart from OPE; estimate matrix elements of four-quark operators by grouping the quark fields intotwo that mediate B → D, and two that candescribe vacuum → π — Are gluons connectingB&D to π either calculable or power suppressed?
• “Naive” factorization: 〈Dπ|cbud|B〉 ∼ FB→D fπSince B and D are “soft” and π is “collinear”, “color transparency” provides aphysical picture for factorization (early 90’s: Bjorken; Dugan, Grinstein)
Configuration of brown muck in D changes only slightly, π is a fast color dipole
This picture expected to hold for B → D(∗)X, as long as EX/mX � 1
Cannot be the full story: Wilson coefficients (of cbud operators) scale dependent
Z L — SSI p.3/11
Factorization in b→ c (cont.)
• “Generalized” factorization: 〈Dπ|cbud|B〉 ∼ FB→D∫ 1
0dxT (x, µ)φπ(x, µ)fπ
(proposed: Politzer, Wise; 2-loop proof: Beneke, Buchalla, Neubert, Sachrajda; all orders proof: Bauer, Pirjol, Stewart)
Fully consistent formulation, scale and scheme dependence cancels order-by-order between Wilson coefficients Ci(µ) and matrix elements 〈Oi(µ)〉
No OPE — corrections presumed to beO(Λ/mb)n but this is not firmly established(Depends on details of B, D, π wave-functions)
Proof applies when meson that inherits the spectator quark from the B is heavyand the other is light
• Factorization also holds in the large number of colors limit(Nc → ∞ with αsNc = const.) in all B0 → M−1 M
+2 type
decays, corrections ∝ 1/N2c
(a) (b)
(c)
B0 M−1
Z L — SSI p.3/12
Factorization tests
• Factorization has been observed to work in B0 → D(∗)+ π− decays at the <∼ 10%level (in amplitudes) ...it gets really interesting just below this (∼ 1/N2
c )
Want to understand quantitatively accuracy of factorization in different processes
• ∼ 35% corrections for B− matrix elements have been observedSpectator in B going into π expected to be power suppressed
� � � �π− D0
B−
B0, B− D0, D+ π−
B(B− → D0π−)B(B0 → D+π−)
= 1 +O(ΛQCD/mc,b) , data: ∼ 1.8± 0.2
Ratio appears universal across channels (D/D∗, π/ρ)
Z L — SSI p.3/13
Isospin again: B → Dπ
• Classify amplitudes in terms of isospin (conserved by strong interaction) insteadof “tree” and “color suppressed tree”, etc.
Two isospin amplitudes for B decay to (Dπ) in If = 12 or If = 3
2
Three measurable rates ⇒ 1 relation:
A(B− → D0π−) = A(B0 → D+π−) +√
2A(B0 → D0π0)
• Three rates determine |A1/2|, |A3/2| and their relative strong phase
δ ∼ 30◦ (CLEO, Belle, Babar)
QCD factorization predicts δ ∼ O(ΛQCD/mc,b)
Not clear yet what sets the scale for the size of corrections
Z L — SSI p.3/14
Origin of factorization?
• The color transparency argument relies on M2 being fast (m/E � 1); the large-Nc argument is independent of this
Would be nice to observe deviations that clearly distinguish between expectations
– At the level of existing data, factorization also works in B → D(∗)s D(∗) when
both particles are heavy
– Check if factorization is worse in B0 → D(∗)−s π+ than in B0 → D(∗)+ π− ?
Need B → π form factor ↖ should be |Vub/Vcb|2× power suppressed
– “Designer mesons”: Study factorization breaking in decays that vanish in naivefactorization (so αs & 1/m corrections important), e.g, B0 → D(∗)+ a0/b1/π2
Rates at 10−6 level — soon accessible? (Diehl & Hiller)
Z L — SSI p.3/15
Factorization in B → D(∗)X
• Study accuracy as a function of the kinematics, with fixed multi-body final states
Expect some nonperturbative corrections to grow as mX increases (ZL, Luke, Wise)
Compare B → D∗4π with τ → 4π (allows 0.4 <∼ mX/EX <∼ 0.7)
0.5 1 1.5 2 2.5 3�
3.5
0
0.05
0.1
0.15
0.2
0.5 1 1.5 2 2.5 3�
3.5
0
0.01
0.02
0.03
0.04τ decay prediction (4π)− (ωπ)−
B decay data
Observing deviations that grow with mX would provideevidence that perturbative QCD is an important part ofthe success of factorization in B → D∗X
Different charge modescan disentangle back-grounds from D∗∗, etc.
(CLEO)
bW- u
d}d }D +
d
{Bo
*
(a)
bW- u
d}d c}D o
d
{Bo
*
(b)
b
W- ud
}d
}D o
d
{Bo*
(c)
c
c
Z L — SSI p.3/16
Factorization in charmless decays
Factorization in charmless B decays
• Two contributions:
B
π
π B π
π
Two proposals:(1) “QCD factorization:” (Beneke, Buchalla, Neubert, Sachrajda)
〈ππ|Oi|B〉 ∼ FB→π T (x)⊗ φπ(x) + T (ξ, x, y)⊗ φB(ξ)⊗ φπ(x)⊗ φπ(y)
– Sudakov suppression at the b mass scale is not effective in the endpointregions of quark distributions
– Two terms have same size in ΛQCD/mb power counting
– Second term suppressed by αs(mb)
– Small strong phases
Z L — SSI p.3/17
Factorization in charmless B decays
• Two contributions:
B
π
π B π
π
Two proposals:(2) “Perturbative QCD:” (Keum, Li, Sanda)
〈ππ|Oi|B〉 ∼ 0 + T (xi, bi)⊗ φB(x3, b3)⊗ φπ(x2, b2)⊗ φπ(x1, b1)
– Sudakov suppression effective in the regions xi ∼ ΛQCD/mb and 1/bi ∼ ΛQCD
– kT factorization, 1/bi ∼√
ΛQCDmb dominates
– Larger strong phases, annihilation & penguin contributions
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Main issues
Huge body of literature due to importance for CP violation
– Power counting depends on treatment of Sudakovs
BBNS: form factors are nonperturbative inputs
KLS: Sudakov suppression renders form factors calculable
– Some formally O(ΛQCD/mb) terms in BBNS are known to be large
Chirally enhanced terms: 2m2K/mbms ∼ 1
– Other issues raised:Charming penguins (Ciuchini et al.)
Intrinsic charm (Brodsky & Gardner)
Scale where π form factor becomes asymptotic ∼ x(1− x)
It very hard to test the assumptions ... need large variety of rates and direct CPV,for some of which the predictions differ
Z L — SSI p.3/19
B → hh rates vs. predictions
(Nir @ ICHEP)
Although the starting points, and predictions for direct CPV and phases in P/T
differ, both BBNS and KLS can reproduce these rates by now
Experimental data is crucial
Z L — SSI p.3/20
(ρ, η) using charmless rates
Inputs: B → ππ/Kπ rates + BBNS
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Constraint Br+Acp + BBNS confidence level
CK Mf i t t e r
R&D
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γ from Bd,s→ hh
• B → Kπ/ππ: Combination of rates — careful
Need some assumptions on (some of): rescattering effects, penguins, factoriza-tion, SU(3)
• Bd → π+π− vs. Bs → K+K−: see: F. Wurthwein’s talk tomorrow (Fleischer)
Idea: two decays related by u-spin, that exchanges d↔ s
Corrections to the u-spin limit are order ms/Λ, just as for SU(3)Need to constrain it somehow from other measurements
My feeling / hope: measure all possible Bd,s → ππ, Kπ, KK asymmetries andrates, we’ll figure out something, build a case...
Z L — SSI p.3/22
Summary — factorization
• In decays such as B0 → D(∗)+ π− factorization has become well established
• Some power suppressed corrections (formally order ΛQCD/mc) appear sizable
No evidence yet of factorization becoming a worse approximation in B → D(∗)X
as mX increases
• In charmless decays there are two approaches to factorization, BBNS and KLS
• Different assumptions and power counting, and sometimes different predictionsTesting the assumptions in a conclusive way does not seem easy
• Theoretical progress in understanding semileptonic form factors in the small q2
region may help to understand importance of Sudakov effects
• New and more precise data will be crucial to test factorization and tell us aboutsignificance of unknown power suppressed terms in various processes
Z L — SSI p.3/23
Summary
Final remarks
• To overconstrain CKM, all possible clean measurements are very important, bothCP violating and conserving, even if redundant in SM (correlations important)
• The key processes are those which give clean information on short distanceparameters ...one theoretically clean measurement is worth ten dirty ones
• It changes with time what is theoretically clean — significant recent progress for:
– Determination of |Vub| from inclusive B decay
– Exclusive rare & semileptonic form factors at small q2
– Factorization in certain nonleptonic decays
• Studying CKM/CPV and hadronic physics is complementary; except for a few veryclean cases several measurements needed to minimize theoretical uncertainties— data will help to get rid of nasty things hard to constrain otherwise
Z L — SSI p.3/24
A (near future & personal) best buy list
• |Vtd/Vts|: Tevatron should nail this, hopefully very soon (lattice caveats?)
• Rare decays: B → Xsγ near theory limited; q2 distribution in B → Xs`+`− will
be very interesting
• |Vub|: reaching <∼ 10% would be very significant (assumes understanding |Vcb|;a Babar/Belle measurement that may well survive LHCB/BTeV)
• β: reduce error in φKS, η′KS (and D(∗)D(∗)) modes
• βs: is CPV in Bs → ψφ small?
• α: how small is B → π0π0? How big are other resonances in ρ−π Dalitz plot?
• γ: clean modes hard, test SU(3) relations, factorization and other approaches
• try B → `ν, search for “null observables” [aCP (b→ sγ), etc.], for enhancementof B → `+`−, etc.
(apologies for omissions!)
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Conclusions
• The CKM picture is predictive and testable — it passed its first nontrivial testand is probably the dominant source of CPV in flavor changing processes
• The point is not only to measure the sides and angles of the unitarity triangle,(ρ, η) and (α, β, γ), but to probe CKM by overconstraining it in as many waysas possible (rare decays, correlations!)
• The program as a whole is a lot more interesting than any single measurement;all possible clean measurements are important, both CPV and CPC
• Many processes can give clean information on short distance physics, andthere is progress towards being able to model independently interpret manyinteresting observables
“This is not the end. It is not even the beginning of the end.
But it is, perhaps, the end of the beginning.”
— W. Churchill (Nov. 10, 1942)
Z L — SSI p.3/26
